Atmospheric turbulence models are often beneficial for the design and safety compliance of aerospace vehicles. For instance, such models are often used for the design of inlet/engine and flight controls, as well as for studying coupling between the propulsion and the vehicle structural dynamics for supersonic vehicles. Models based primarily on the Kolmogorov spectrum have been previously utilized to model atmospheric turbulence. The Kolmogorov spectrum has an energy level that approaches infinity as frequency approaches zero. This characteristic makes it difficult to implement conventional models in the time domain. The Kolmogorov model has also been extended in the Tank model to develop a baseline of atmospheric turbulence for the High Speed Civil Transport (HSCT). The Tank model also covers atmospheric acoustic wave disturbance modeling utilizing the von Karman spectral.
An approximation of the Kolmogorov model that is commonly used with a finite energy spectrum is the von Karman type model. However, simulating the von Karman type models in the time domain may be difficult due to the fractional order of von Karman type models.
Some have used Dryden model approximation to the fractional order von Karman atmospheric model. However, the Dryden model is second order compared to the 5/3 fractional order of the acoustic velocity atmospheric turbulence spectral. Thus, the Dryden model underestimates the atmospheric disturbance, and does so increasingly with higher frequency. As such, the faster an aerospace vehicle travels, the more the Dryden model will underestimate the atmospheric disturbance. Accordingly, a more accurate model for simulating atmospheric disturbances may be beneficial.